Question: Solve for $x$ and $y$ using substitution. ${-5x-y = 11}$ ${y = -x-3}$
Solution: Since $y$ has already been solved for, substitute $-x-3$ for $y$ in the first equation. ${-5x - }{(-x-3)}{= 11}$ Simplify and solve for $x$ $-5x+x + 3 = 11$ $-4x+3 = 11$ $-4x+3{-3} = 11{-3}$ $-4x = 8$ $\dfrac{-4x}{{-4}} = \dfrac{8}{{-4}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -x-3}\thinspace$ to find $y$ ${y = -}{(-2)}{ - 3}$ $y = 2 - 3$ $y = -1$ You can also plug ${x = -2}$ into $\thinspace {-5x-y = 11}\thinspace$ and get the same answer for $y$ : ${-5}{(-2)}{ - y = 11}$ ${y = -1}$